Let A 0 0 3 1 Find an invertible matrix P and a diagonal ma

Let A = [0 0 3 1]. Find an invertible matrix P and a diagonal matrix D such that A = PDP^-1. P = D =

Solution

A = [ 0 3

       0   1 ]

Eigen values of A : [A - xI] =0

; x= 0,1

Diagonal matrix , D = [ 1 0

                                 0 0 ]

Eigen vectors for x = 0 ; [ 1

                                        0 ]

Eigen vector for x= 1 ; [ 3

                                     1 ]

P = [3 1

       1   0 ]